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math.CO2013★ 6 cited
Calculating Ramsey numbers by partitioning coloured graphs
Alexey Pokrovskiy
In this paper we prove a new result about partitioning coloured complete graphs and use it to determine certain Ramsey numbers exactly. The partitioning theorem we prove is that fo…
math.CO2013★ 11 cited
A linear bound on the Manickam-Miklos-Singhi Conjecture
Alexey Pokrovskiy
Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of k numbers from {x_1, ..., x_n} must have nonnegative sum? Manickam, Miklos, and…